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A274042
Numbers n such that n - 53, n - 1, n + 1, n + 53 are consecutive primes.
1
9401700, 64312710, 78563130, 83494350, 92978310, 101520540, 111105090, 121631580, 136765860, 138330780, 139027950, 145673850, 157008390, 163050090, 166418280, 169288530, 170473410, 177920850, 198963210, 200765250, 213504870, 220428600
OFFSET
1,1
COMMENTS
This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
The numbers n - 53 and n + 1 belong to A204665 (p such that p + 52 is the next prime).
The numbers n - 53 and n - 1 belong to primes p such that p + 54 is prime.
LINKS
Eric Weisstein's World of Mathematics, Twin Primes
EXAMPLE
9401700 is the average of the four consecutive primes 9401647, 9401699, 9401701, 9401753.
64312710 is the average of the four consecutive primes 64312657, 64312709, 64312711, 64312763.
MATHEMATICA
Select[Partition[Prime[Range[122*10^5]], 4, 1], Differences[#]=={52, 2, 52}&][[All, 2]]+1 (* Harvey P. Dale, Mar 07 2018 *)
PROG
(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 250000001, 6):
..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-53 and nextprime(i+1) == i+53: print (i, end=', ')
CROSSREFS
Cf. A014574, A077800 (twin primes), A249674, A256753.
Sequence in context: A328207 A069376 A281570 * A066703 A270994 A162030
KEYWORD
nonn
AUTHOR
Karl V. Keller, Jr., Jun 07 2016
STATUS
approved